When you have a time series that contains both trend and seasonal components, I learned that either seasonal decomposition (e.g., forecast the deseasonalized series, then add back the seasonal factor to obtain forecasts of the original series) or Holt-Winters methods (additive or multiplicative) can be used for forecasting (or just data fitting) purposes.

Is there a general rule (or merely observation) when seasonal decomposition should be preferred to HW? I personally feel like HW is easier to use, and more responsive to changes in later observations. I read that seasonal decomposition is useful for macroeconomic data. But since the seasonal factors in the decomposition are calculated from past data, and they are constant for each season index throughout the series (this is true for the basic decomposition method I read from a textbook, but not sure if it's true for other decomposition methods), I'm not sure how good it would be for forecasting purpose. Should seasonal decomposition be considered when trying to forecast a seasonal series? If so, for which type of series would it work best?

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#### Best Answer

I am not aware of such a rule of thumb. One problem is that decomposition is motivated by the fact that it works and that it is simply to explain, not by an underlying statistical model, so we can't (say) compare likelihoods or similar.

I'd recommend that you use a holdout sample at the end. Fit the two competing approaches to the rest of the data, forecast into the holdout sample, check which one has the lower error, and go with that method.

Alternatively, use *both* approaches. Calculate forecasts for both and then average them within each time bucket. A common finding in forecasting (and other predictive applications) is that averaging, or "ensemble methods", works better than trying to identify the optimal method *ex ante*. However, this effect is strongest if the candidate methods are dissimilar, and the difference between seasonal decomposition and Holt-Winters is not really all that great, so I don't know whether this will have a big impact here.

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